Highest Common Factor of 258, 914 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 258, 914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 258, 914 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 258, 914 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 258, 914 is 2.
HCF(258, 914) = 2
HCF of 258, 914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 258, 914 is 2.
Highest Common Factor of 258,914 is 2
Step 1: Since 914 > 258, we apply the division lemma to 914 and 258, to get
914 = 258 x 3 + 140
Step 2: Since the reminder 258 ≠ 0, we apply division lemma to 140 and 258, to get
258 = 140 x 1 + 118
Step 3: We consider the new divisor 140 and the new remainder 118, and apply the division lemma to get
140 = 118 x 1 + 22
We consider the new divisor 118 and the new remainder 22,and apply the division lemma to get
118 = 22 x 5 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 258 and 914 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(118,22) = HCF(140,118) = HCF(258,140) = HCF(914,258) .
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Frequently Asked Questions on HCF of 258, 914 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 258, 914?
Answer: HCF of 258, 914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 258, 914 using Euclid's Algorithm?
Answer: For arbitrary numbers 258, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.